Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20261458 | C2 | semidirect |
| 3. #20261082 | C2 | semidirect |
| 4. #20261062 | C2 | semidirect |
| 5. #20261020 | C2 | semidirect |
| 6. #20260967 | C2 | semidirect |
| 7. #20260935 | C2 | semidirect |
| 8. #20260896 | C2 | semidirect |
| 9. C8×D388 | C2 | semidirect |
| 10. #20260730 | C2 | semidirect |
| 11. C4×Q16×C97 | C2 | semidirect |
| 128. C97 | #3304 | semidirect |
| 137. C4×Q16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261458 | 2 |
| #20261407 | 2 |
| #20261082 | 2 |
| #20261062 | 2 |
| #20261020 | 2 |
| #20260967 | 2 |
| #20260935 | 2 |
| #20260896 | 2 |
| C8×D388 | 2 |
| #20260730 | 2 |
| C4×Q16×C97 | 2 |
| #3304 | 97 |